Spectral gap for the interchange process in a box.
Spontaneous breaking of continuous rotational symmetry in two dimensions.
Standard stochastic coalescence with sum kernels.
State classification for a class of interacting superprocesses with location dependent branching.
State dependent multitype spatial branching processes and their longtime behavior.
Stationary measures and phase transition for a class of probabilistic cellular automata
We discuss various properties of Probabilistic Cellular Automata, such as the structure of the set of stationary measures and multiplicity of stationary measures (or phase transition) for reversible models.
Stationary measures and phase transition for a class of Probabilistic Cellular Automata
We discuss various properties of Probabilistic Cellular Automata, such as the structure of the set of stationary measures and multiplicity of stationary measures (or phase transition) for reversible models.
Statistical study of Navier-Stokes equations, I
Steady state and scaling limit for a traffic congestion model
In a general model (AIMD) of transmission control protocol (TCP) used in internet traffic congestion management, the time dependent data flow vector x(t) > 0 undergoes a biased random walk on two distinct scales. The amount of data of each component xi(t) goes up to xi(t)+a with probability 1-ζi(x) on a unit scale or down to γxi(t), 0 < γ < 1 with probability ζi(x) on a logarithmic scale, where ζi depends on the joint state of the system x. We investigate the long time behavior, mean field...
Stein’s method in high dimensions with applications
Let be a three times partially differentiable function on , let be a collection of real-valued random variables and let be a multivariate Gaussian vector. In this article, we develop Stein’s method to give error bounds on the difference in cases where the coordinates of are not necessarily independent, focusing on the high dimensional case . In order to express the dependency structure we use Stein couplings, which allows for a broad range of applications, such as classic occupancy,...
Stochastic approximations of the solution of a full Boltzmann equation with small initial data
Stochastic approximations of the solution of a full Boltzmann equation with small initial data
This paper gives an approximation of the solution of the Boltzmann equation by stochastic interacting particle systems in a case of cut-off collision operator and small initial data. In this case, following the ideas of Mischler and Perthame, we prove the existence and uniqueness of the solution of this equation and also the existence and uniqueness of the solution of the associated nonlinear martingale problem. Then, we first delocalize the interaction by considering a mollified Boltzmann...
Stochastic coalescence.
Stochastic domination : the contact process, Ising models and FKG measures
Stochastic dynamics macroscopically governed by the porous medium equation for isothermal flow.
Stochastic foundations of the universal dielectric response
We present a probabilistic model of the microscopic scenario of dielectric relaxation. We prove a limit theorem for random sums of a special type that appear in the model. By means of the theorem, we show that the presented approach to relaxation phenomena leads to the well known Havriliak-Negami empirical dielectric response provided the physical quantities in the relaxation scheme have heavy-tailed distributions. The mathematical model, presented here in the context of dielectric relaxation, can...
Stochastische Bewegungen und ihre ersten Integrale.
Strict convexity of the limit shape in first-passage percolation.
Strong hydrodynamic limit for attractive particle systems on .
Strong law of large numbers for the interface in ballistic deposition